1. Field of the Invention
The invention relates generally to the field of seismic data processing. More particularly, the invention relates to methods for producing seismic images of the Earth's subsurface using prestack depth migration.
2. Background Art
Seismic surveying is used to evaluate structures of, compositions of, and fluid content of subsurface earth formations. A particular application for seismic surveying is to infer the presence of useful materials, such as petroleum, in the subsurface earth formations. Generally, seismic surveying includes deploying an array of seismic sensors at or near the Earth's surface, and deploying a seismic energy source near the sensors also at or near the surface. The seismic energy source is actuated and seismic energy emanates from the source, traveling generally downwardly through the subsurface until it reaches one or more acoustic impedance boundaries. Seismic energy is reflected from the one or more impedance boundaries, where it then travels upwardly until being detected by one or more of the sensors. Structure and composition of the subsurface is inferred from the travel time of the seismic energy, and the amplitude and phase of the various frequency components of the seismic energy with respect to the energy emanating from the seismic source.
One class of methods for processing seismic data is known as prestack migration. In processing seismic survey data using prestack migration methods, conceptually energy propagation through the Earth's subsurface may be thought of as follows. Energy from all seismic energy sources used in producing a survey propagates from a subsurface “scatter point” to all the seismic receivers used in acquiring seismic data. Consequently, all recorded traces (called “input” traces for purposes of seismic processing) can contain energy from a particular scatter-point. Because the input traces have a finite recording time, the scattered energy is restricted to traces within the prestack migration “aperture” of the scattering point. An objective of prestack migration is to gather the seismic energy from all the recorded traces within the prestack migration aperture and sum it back to the scatter-point location.
The accuracy of the migration is related to the accuracy of the calculated seismic signal travel times that are used for migrating the data. The key point is to calculate accurate travel times in order to have better migration imaging. In homogeneous media, seismic travel times, as functions of offset (equivalent distance between the source and receiver along the surface) and common imaging point (“CIP”), are determinable by a simple analytical equation, commonly referred to as the double-square root (“DSR”) equation. The DSR equation to compute travel times is fundamental in migration. The DSR equation is exact in the sense that there are no error-terms dependent on dip angle and offset angle.
The estimation of interval velocities in the depth domain is required to perform prestack depth migration in isotropic media. Travel time tomography is a preferred method to estimate the interval velocities. However, it has been recognized that when the seismic velocities are affected by anisotropy, the results from prestack depth migration may not be accurate. If anisotropy is ignored in migration processing, positioning of the seismic events in space will be incorrect and energy “focusing” after migration will not be optimum. The foregoing two factors may have important exploration implications, for example, the depths at which formation boundaries are determined to occur by drilling wells through the subsurface may not correspond in depth to formation boundaries determined by processing the seismic data.
A common type of anisotropy is known as vertically transverse isotropy (“VTI”). A medium such as a formation having VTI is described by three parameters: Vo (interval vertical velocity); ε and δ. The latter two parameters are known as “Thomsen's parameters.” Thomsen's parameters are described in, Thomsen, Leon A, Weak elastic anisotropy, Geophysics, 51, 1954-1966, Society of Exploration Geophysicists (1986).
In three dimensional (“3D”) tomography in VTI media, the parameters Vo, ε and δ, may be determined in different ways, for example, the parameters may be related to Vnmo (interval normal moveout (“NMO”) velocity), Vo (interval vertical velocity) and interval η (the interval anelliptic parameter). See, for example, U.S. Pat. No. 6,985,405 to Ren et al. and assigned to the assignee of the present invention. Vnmo and interval η can be related to Thomsen's parameters (δ and ε) by the following expressions:
                                          V            nmo                    =                                    V              o                        ⁢                                          1                +                                  2                  ⁢                  δ                                                                    ;                            (        1        )                        and                                                      η        =                              ɛ            -            δ                                1            +                          2              ⁢              δ                                                          (        2        )            
Performing 3D tomographic velocity estimation for VTI media requires estimating either the variables Vo, δ and ε, or the variables Vo, Vnmo and interval η. Estimating either set of parameters above is theoretically equivalent to estimating the other set based on equations (1) and (2), however, estimating may result in ambiguous solutions for the three parameters Vo, δ and ε if only compressional-wave (P-wave) seismic data are available. See, Tsvankin, I., and L. Thomsen, Inversion of reflection travel times for transverse isotropy. Geophysics, 60, no. 4, 1095-1107, Society of Exploration Geophysicists, 1995.
3D tomographic velocity estimation in VTI media has been described in Zhou, H., Pham, D. Gray, S. and Wang, B., 3-D tomographic velocity analysis in transversely isotropic media, 73rd SEG annual technical conference (2003), Expanded Abstracts and Yuan, J., Ma, X., Lin, S., and Lowrey, D., P-wave tomographic velocity updating in 3D inhomogeneous VTI media, 76th SEG annual technical conference (2006), Expanded Abstracts.
There continues to be a need for improved estimation of interval velocities and interval anisotropy parameters for prestack depth migration of seismic data.